In this example, we will compare the deconstruct method and the traditional methodfor solving a linear equation in one variable.
However, it is important to recognize as we use either method,we are always performing the same operation to bothsides of the equation, which creates an equivalent equation.
Let's first solve the equationusing the deconstruct method, also referred to as thestory of the variable method.
For this method, thefirst step is to construct the story of the variablethat creates the equation, and then step two, deconstructthe story of the variable and then three, applythe deconstruct story to both sides of the equationto solve the equation, and step four, check the solution.
However, this method does have issues when we have equationsin the form shown here, where if the variable term is not first, we would need to rewrite the equation so the variable term isfirst as a variable equation.
There's also issues whenthere are variable terms on both sides of the equation.
Once again, we would haveto rewrite the equation as an equivalent equationwhere the variable term is the first term on theleft side or right side of the equation.
For this reason, it mightbe helpful at this point to transition to themore traditional method of solving linear equations.
For this method, thereis an option to multiply both sides of the equation to clear any fractions or decimals, but in general, the first step is to simplifyeach side of the equation by clearing parenthesesand combining like terms, then step two, add or subtractto isolate the variable term on one side, and stepthree, multiply or divide both sides of the equationto isolate the variable and solve the equation.
And then again, stepfour, check the solution.
Let's first solve the equationusing the deconstruct method.
We begin by determiningthe construction story.
So beginning with the variable, m, we first multiply by three to get three m.
Step two, we subtract oneto get this difference.
Step three, then multiplyby four to get this product, and then step four is toadd seven to get this sum, and then the result is negative 13.
For the deconstruction story,we need to undo these steps of the constructionstory in order to solve the equation for m.
For the deconstruct story,we first undo adding seven by subtracting seven, thenwe undo multiplying by four by dividing by four, then weundo the subtraction of one by adding one, and finally,we undo this multiplication involving three by dividingboth sides by three.
So applying the deconstructstory, the first step is subtract seven from bothsides of the equation.
Simplifying both sides of the equation, seven minus seven is zero.
We now have the equivalent equation four times the quantitythree m minus one equals negative 13 minus seven is negative 20.
The next step is to divide both sides of the equation by four.
Simplifying, four dividedby four simplifies to one.
We now have the equivalent equation three m minus one equalsnegative 20 divided by four is negative five.
To undo the subtraction, we add one to both sides of the equation.
Simplifying, negativeone plus one is zero.
We now have the equation three m equals negative five plusone equals negative four.
And the last step is toundo multiplying by three by dividing both sides by three.
Simplifying, threedivided by three is one, one times m is m, our solutionis m equals negative 4/3.
Now let's solve the equation again using a more traditional method.
Step one is to simplifyboth sides of the equation, which means for this equation,we begin by distributing the four for the parenthesesand then we combine like terms.
So four times three m is12m, minus four times one, so that's minus four plusseven equals negative 13.
We can still simplify the left side by combining the like termsor the constant terms.
Negative four plusseven is positive three.
The equation simplifies to 12m plus three equals negative 13.
The next step is toisolate the variable term by adding or subtracting.
We need to undo the plusthree by subtracting three on both sides of the equation.
Simplifying, three minus three is zero.
The equation simplifies to 12m equals negative 13 minus three is negative 16.
The last step is to multiplyor divide this all for m.
12m means 12 times m, thelast step is to divide both sides by 12.
Simplifying, 12 dividedby 12 is equal to one, one times m is m.
We have m equals negative 16/12, but this fraction does simplify.
The greatest common factorbetween 16 and 12 is four.
To simplify, we divide thenumerator and denominator by four, which does giveus m equals negative 4/3.
So we do get the same solution.
Again, the importantthing to remember here is that for both methods, wedid perform the same operation to both sides of theequation, each time getting an equivalent equation.
Now to verify this solutionis correct, we need to substitute negative 4/3for m into the equation to make sure it satisfies the equation.
For this example, let'suse the calculator.
We will evaluate theleft side of the equation to make sure it's equal to negative 13.
So we enter four open parenthesis three and then times negative 4/3, so open parenthesis negativefour divided by three close parenthesis and we have minus one close parenthesis plus seven and enter and notice how the leftside of the equation is equal to negative 13 whenm is equal to negative 4/3, verifying our solution is correct.
I hope you found this helpful.